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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Sharp Hessian integrability estimates for nonlinear elliptic equations: An asymptotic approach

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Pimentel, Edgard A. ; Teixeira, Eduardo V.
Total Authors: 2
Document type: Journal article
Source: JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES; v. 106, n. 4, p. 744-767, OCT 2016.
Web of Science Citations: 5

We establish sharp W-2,W-p regularity estimates for viscosity solutions of fully nonlinear elliptic equations under minimal, asymptotic assumptions on the governing operator F. By means of geometric tangential methods, we show that if the recession of the operator F - formally given by F{*} (M) := infinity(-1) F(infinity M) - is convex, then any viscosity solution to the original equation F(D(2)u) = f(x) is locally of class W-,(2,p) provided f is an element of L-P, p > d, with appropriate universal estimates. Our result extends to operators with variable coefficients and in this setting they are new even under convexity of the frozen coefficient operator, M bar right arrow F(x(0), M), as oscillation is measured only at the recession level. The methods further yield BMO regularity of the Hessian, provided the source lies in that space. As a final application, we establish the density of W-2,W-p solutions within the class of all continuous viscosity solutions, for generic fully nonlinear operators F. This result gives an alternative tool for treating common issues often faced in the theory of viscosity solutions. (C) 2016 Elsevier Masson SAS. All rights reserved. (AU)

FAPESP's process: 14/15795-1 - Geometric and analytic aspects of the theory of nonlinear partial differential equations
Grantee:Alexandre Nolasco de Carvalho
Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
FAPESP's process: 15/13011-6 - Nonlinear Partial Differential Equations: Well-Posedness and Regularity Theory
Grantee:Edgard Almeida Pimentel
Support Opportunities: Regular Research Grants